25,270 Answered Questions for the topic calculus

Calculus

02/09/24

Derivatives and tangent line
One can draw a diagram to show that there are two tangent lines to the parabola y=x^2+1 that pass through the point (0,-3) . Find the x-coordinates of the points where these tangent lines intersect... more
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Calculus

02/09/24

The doubling period of a bacterial population is 20 minutes. At time t =120 minutes, the bacterial population was 80000.

what was the initial population at time t= 0? find the size of the bacterial population after 4 hours
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Calculus

02/09/24

Evaluate the integral
∫dx/(x2√(9+x2))
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Calculus

02/09/24

Evaluate the integral
∫x5√(1-x2)dx
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Calculus

02/09/24

Evaluate the integral
∫tan4xsec4xdx
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02/09/24

Solve for X (Linear Algebra)
I keep getting this question wrong and I have no idea how to do this. It would be really appreciated if you can help me. Here's the link to the example: https://ibb.co/pjTMyg2
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Calculus

02/09/24

Integration By Parts Calculus Question
Find the integral ∫(x^pi)(lnx) dx using integration by parts. Carefully explain all steps.
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Calculus

02/08/24

For the function y = 9x^2, find the following
a) the instantaneous rate of change of f(x) at the value x = 1
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Calculus

02/08/24

Given f(x) = −7 + x2, calculate the average rate of change on each of the given intervals.
(a)The average rate of change of f(x) over the interval [−4, −3.9]  is (b)The average rate of change of f(x) over the interval [−4, −3.99]  is (c)The average rate of change of f(x) over the... more
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Calculus

02/08/24

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 + x − 9 = 0, (1, 2)
on the closed interval [1,2] , f(1)= and f(2)=
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Calculus

02/08/24

If 2x − 1 ≤ f(x) ≤ x2 − 2x + 3 for x ≥ 0,

find lim f(x)x→2
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Calculus

02/08/24

From the top of a building 48 feet high, a ball is thrown upward with an initial velocity of 48 feet per second.
From the top of a building 48 feet high, a ball is thrown upward with an initial velocity of 48 feet per second.(a) When does it reaches its maximum height? when t= ____ seconds(b) What is its... more
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Calculus

02/08/24

find the point x
find the point x, 0 x 1, on the graph of y = sin2(3x) where the tangent line is horizontal.x = 
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Calculus

02/08/24

Suppose an object is moving along a horizontal coordinate line with distance formula
Suppose an object is moving along a horizontal coordinate line with distance formulas(t) = t3 - t2 (in feet）where t ≥ 0 is in seconds.(a) Find the velocity v(t) and acceleration a(t)• Include... more
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Calculus

02/08/24

Find the derivatives for each of the following functions. Show your work properly!
Find the derivatives for each of the following functions. Show your work properly! f(x) = 1/(x3 -3x + 7)8 g(t) = sin (πt6) (t + 9)3. h (y) = y cos7(2y) + sin(y)/ 3y2 - 2
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Calculus

02/08/24

Consider the function f(x)= 1/2 cos(2x)

1. Consider the function f(x)= 1/2 cos(2x) (a) Compute ( f’(x) (b) Find an equation for the tangent line to the graph of f(x) at x= π/3 (c) Compute f(11)(x).
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Calculus Python

02/07/24

Given f(x) = 3^3x − 1/12x
Use a for loop (list comprehension) to evaluate the function at x = −0.1, −0.01, −0.001, −0.0001,then at x = 0.1, 0.01, 0.001, 0.0001 to numerically estimate limx→0 f(x).(b) Plot f on the interval... more
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Calculus Precalculus Python

02/07/24

Suppose you want to build a fence around a rectangular enclosure and have 200 yards of material to use.
In addition, suppose there is a long brick wall you can use for one of thesides. Let x denote the length (in yards) of the sides perpendicular to the brick wall.(a) Write the formula for A(x), the... more
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Calculus

02/07/24

find lim x→2 f(x).
If 2x − 1 ≤ f(x) ≤ x2 − 2x + 3 for x ≥ 0, find lim x→2 f(x).
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Calculus

02/07/24

Evaluate the limit, if it exists.
 lim (6/t - 6/t^2 + t ) t→0
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02/07/24

Factor completely over the real numbers 6x5-4x3-16x
Factor completely over the real numbers (the solution is 2x(3x2+4)(x+√2)(x−√2). Please show a step-by step process for solving this problem.1). 6x5-4x3-16x
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Calculus

02/07/24

A real estate company owns 120 apartments which are fully occupied when the rent is $300 per month.
A real estate company owns 120 apartments which are fully occupied when the rent is $300 per month. The company estimates that for each additional $10 a month increase in rent, live apartments will... more
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Calculus

02/07/24

A steel storage tank for propane gas is to be constructed into the shape of a right circular cylinder with a hemisphere on each end.

A steel storage tank for propane gas is to be constructed into the shape of a right circular cylinder with a hemisphere on each end. The construction cost per square foot of the end pieces is twice... more
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Calculus

02/07/24

Find derivative by first principle method
How to find the derivative of cos^-1 x / x by first principle method ?
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02/06/24

Graph help for tranfromation, reflection stuff. PLease help out :)
a graph of f(x)=1/4|cos(pi(x-1/2))-3| Can you tell me all that is happening here including the transformations, reflection, stretch/compression, shifts, etc, and the vertex and x/y values, and how... more
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